closed graph theorem


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closed graph theorem

[¦klōzd ¦graf ′thir·əm]
(mathematics)
If T is a linear transformation on Banach space X to Banach space Y whose domain D (T) is closed and whose graph, that is, the set of pairs (x,Tx) for x in D (T), is closed in X × Y, then T is bounded (and hence continuous).
References in periodicals archive ?
52]), the Open Mapping Theorem and the Closed Graph Theorem (see e.